1. What did the acorn say when he grew up? Points Lines Planes Circles Polygons Congruency Similarity

3. Geometry is a branch of mathematics that deals with points, lines, planes and solids, and examines their properties, measurement, and mutual relationship in space.

4. Geometry was used by ancient Egypt to measure land and build pyramids. The Greeks used a straightedge and a compass to draw lines and circles. They discovered ways to calculate distances without actually measuring them.

5. People in many fields use geometry. For example, engineers, rocket scientists, surveyors, designers, graphic artists, carpenters, astronomers, plumbers, laboratory technologists, advertising copywriters, construction workers, chemists, astronauts, and many more.

6. Geometry is used by anyone who needs to draw a circle, line, or line segment. The name geometry comes from two Greek words: geo, meaning “land,” and metry, meaning “to measure.”

8. A Greek mathematician named Euclid brought together most of the knowledge of geometry. He set down general rules that he called axioms, postulates, and theorems. He published a 13-volume work called The Elements. Euclid’s system of geometry is called Euclidean Geometry. Students study Euclidean Geometry in high school.

9. Other mathematicians who contributed to the formation of geometry are Pythagoras, Gauss, Lewis Carroll, Johannes Kepler, and many others.

10. Points, Lines, and Planes Space-A boundless, three-dimensional set of all points.

11. Coordinate Plane, points, lines, and Planes Identify collinear points. Identify and model points, lines, and planes. Identify coplanar points and intersecting lines and planes.

12. A point has no dimension. It is usually represented by a small dot. A PointA U SING U NDEFINED T ERMS AND D EFINITIONS

13. A line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions. Lineor AB Collinear points are points that lie on the same line. U SING U NDEFINED T ERMS AND D EFINITIONS

14. A plane extends in two dimensions. It is usually represented by a shape that looks like a table or a wall, however you must imagine that the plane extends without end. U SING U NDEFINED T ERMS AND D EFINITIONS

15. Coplanar points are points that lie on the same plane. Plane M or plane ABC A C M B U SING U NDEFINED T ERMS AND D EFINITIONS

16. Naming Collinear and Coplanar Points S OLUTION Points D, E, F lie on the same line, so they are collinear. There are many correct answers. For instance, points H, E, and G do not lie on the same line. Points D, E, F, and G lie on the same plane, so they are coplanar. Also, D, E, F, and H are coplanar. G H F E D Name three points that are collinear. Name four points that are coplanar. Name three points that are not collinear.

17. Another undefined concept in geometry is the idea that a point on a line is between two other points on the line. You can use this idea to define other important terms in geometry. U SING U NDEFINED TERMS AND DEFINITIONS

18. The line segment or segment AB (symbolized by AB) consists of the endpoints A and B, and all points on AB that are between A and B. U SING U NDEFINED T ERMS AND D EFINITIONS Consider the line AB (symbolized by AB).

19. The ray AB (symbolized by AB) consists of the initial point A and all points on AB that lie on the same side of A as point B. Note that AB is the same as BA, and AB is the same as BA. However, AB and BA are not the same. They have different initial points and extend in different directions. U SING U NDEFINED T ERMS AND D EFINITIONS

20. If C is between A and B, then CA and CB are opposite rays. Like points, segments and rays are collinear if they lie on the same plane. So, any two opposite rays are collinear. Segments, rays, and lines are coplanar if they lie on the same plane. U SING U NDEFINED T ERMS AND D EFINITIONS

21. Drawing Lines, Segments, and Rays 1 2 3 4 Draw three noncollinear points J, K, L. Then draw JK, KL and L J. S OLUTION Draw J, K, and L Draw JK. Draw LJ. K L J Draw KL.

22. Drawing Opposite Rays Draw two lines. Label points on the lines and name two pairs of opposite rays. S OLUTION Points M, N, and X are collinear and X is between M and N. So, XM and XN are opposite rays. Points P, Q, and X are collinear and X is between P and Q. So, XP and XQ are opposite rays.

23. S KETCHING I NTERSECTIONS OF L INES AND P LANES Two or more geometric figures intersect if they have one or more points in common. The intersection of the figures is the set of points the figures have in common.

24. Sketching Intersections Sketch a line that intersects a plane at one point. S OLUTION Draw a plane and a line. Emphasize the point where they meet. Dashes indicate where the line is hidden by the plane.

25. Sketch two planes that intersect in a line. Sketching Intersections S OLUTION Draw two planes. Emphasize the line where they meet. Dashes indicate where one plane is hidden by the other plane